Quantum thermodynamic processes: A control theory for machine cycles

TL;DR

This paper develops a control theory framework for quantum thermodynamic processes, demonstrating universal efficiency bounds and analyzing finite-time dynamics of quantum machines with discrete spectra.

Contribution

It introduces a control-theoretic approach to quantum thermodynamics, establishing universal bounds and systematic treatment of non-equilibrium effects in quantum cycles.

Findings

Carnot efficiency as a universal upper bound for quantum cycles

Renormalized variables enable systematic inclusion of non-equilibrium phenomena

Machine operation ceases at large cycle speeds depending on cycle type

Abstract

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this 2-dimensional control plane. Putting aside coherence we show that for a large class of quantum objects with discrete spectra and for the cycles considered the Carnot efficiency applies as a universal upper bound. In the dynamic (finite time) regime renormalized thermodynamic variables allow to include non-equilibrium phenomena in a systematic way. The machine function ceases to exist in the large speed limit; the way, in which this limit is reached, depends on the type of cycle considered.